Levels of 209Po and 211Po populated in one-neutron stripping and pickup from 210Po

I.E.I:

[

Nuclear Physics A314 (1979)101-114; (~North-HollandPublishinoCo.,Amsterdam

2.(;.

I

N o t to be reproduced by photoprint or microfilm without written permission from the publisher

LEVELS OF 2°9p0 AND 211po POPULATED IN ONE-NEUTRON STRIPPING AND PICKUP FROM 210po T. S. BHATIA t and T. R. CANADA *

University of Pittsburgh , Pittsburgh, Pa. 15213 P. D. BARNES and R. A. EISENSTEIN

Carnegie-Mellon University, Pittsburyh, Pa. 15213 and C. ELLEGAARD

Carnegie-Mellon University, Pittsburgh, Pa. 15213 and The Niels Bohr Institute, Copenhagen, Denmark Received 11 August 1978 Abstract: Energy levels of 2°9po have been populated with the 2~°Po(d, t)2°9po and 2t°Po(p, d)2°9po reactions at bombarding energies of 17.0 and 17.8 MeV respectively. Fifteen levels were observed below 2.7 MeV of excitation. Energy levels of 2t~po were populated with the 2~°Po(d, p)2l~po reaction, also at 17.0 MeV. Thirty-five levels, almost all new, were observed below 3.9 MeV of excitation. Comparison of experimental angular distributions with DWBA calculations allowed /-value assignments and extraction of spectroscopic factors for many levels. In 2°9po the observed level structure is well described in terms of a simple particle-vibration coupling model. In 2 ~1Po the level structure is more complex and the simple model is not adequate. NUCLEAR REACTIONS 21°Po(d, t), 21°Po(d, p), E = 17.0 MeV; 21°Po(p, d), E = 17.8 MeV; measured tr(0). 2°9po, 21ip0 deduced levels, 1, J, n, spectroscopic factors. Enriched radioactive target.

1.. Introduction

The present work is part of a systematic study of nuclei in the lead region exploring the concept of elementary excitations 1, 2). This concept has been widely utilized in discussing energy levels and level properties in nuclei like (i) 2°8pb which partly acts as the vacuum state and partly may be excited by collective excitations [see ref. ~)], (ii) the nuclei 2°9pb, 2°9Bi, 2°Tpb and 2°7T1 where the single-nucleon aspects are explored [see the review of ref. 3)], and (iii) nuclei with pairs of nucleons added or removed from 2°8pb as in 2°6pb and 2l°pb where the pairing correlations are explored and the concept of pairing phonon is introduced [see the review of ref. 4)]. * Present address: Los Alamos Scientific Laboratory, Los Alamos, NM 87544. 101

102

T.S. BHAT1A et al.

In the present work we describe results concerning nuclei that have both a pairing phonon and a single particle or hole added to the core. The results are from the (d, p), (p, d) and (d, t) reactions on 2lOpo and thus relate to the single-particle properties of the nuclei 2 ° 9 p o and 2~po. By comparing the results with results of the same reactions on 2°spb, we may study the effect of the extra proton pair in 2 ~Opo on the singleparticle spectrum. Nuclei of similar structure have been studied in earlier works namely 2°9T1 and 211pb [ref. 5)] and 2°Spb [ref. 6)].

2. Experiment The experimental setup has been described in an earlier paper ~), so only a short summary is given here. A target of ~ 100 #g/cm 2 2~Opo(95 ~o) metal on a 50 ~g/cm 2 carbon foil, was bombarded with deuterons and protons from the two-stage tandem facility at the University of Pittsburgh. Deuterons of 17 MeV were used for the (d, p) and (d, t) reactions, and protons of 17.8 MeV for the (p, d) reactions. The energy 17.8 MeV Was chosen for the protons in order to avoid interference from the analog resonances which would occur in the proton entrance channel at energies below 17 MeV. The reaction products were momentum analyzed in a split pole a) magnetic spectrograph and detected in Kodak NTB photographic emulsions. The plates were covered with aluminum foils of thicknesses choosen to stop unwanted particles where possible [the (d, p) reaction] or to degrade the energy of the detected particle to maximum ionization [(d, t) and (p, d) reactions]. Relative cross sections for different angles were obtained by monitoring elastically scattered deuterons in two sodium iodide detectors at fixed angles. Absolute cross sections were obtained for the deuteron exposures by measuring elastically scattered deuterons at small angles in short exposures, and also by comparing the yield with that obtained from a 2°apb target of known thickness. The accuracy of the absolute cross section is estimated to 15 ~o. For the proton exposures only relative cross sections were obtained.

3. Experimental results and analysis 3.1. THE (d, p) REACTION

Two exposures were made with deuterons at each angle for angles greater than 36°. A short one ( ~ 1000 pC) in which the strongest peaks were scannable, and a long one (,.~ 10000/~C) to obtain the cross section for small peaks with good statistics. An example of the proton spectra obtained is given in fig. 1. The peaks labeled with bold numbers are those identified as peaks from the 2~Opo(d' p)211po reaction. The excitation energies of the corresponding levels in 211po are given in table 1. Angular distributions of the protons from the various levels are shown in figs. 2 4 for all but the very weakest populated levels. In order to identify the l, value for the transferred neutron to the levels in 21 ipo

2 0 9 p o ' 21 ipo

103

EXCITATION ENERGY (MeV) 2 I ? 350 ]~

J

23 iSl

300

i

1

0

zlo Po (d,p)Z" Po

o

Ed = 170 MeV

e =130"Long run

250

|

I

¢~ 200

SJ

s=

-

2

uJ ~. m

1'/ 150

n~,

-

~

1

33

SI

100

50

40

45 50 DISTANCE ALONG PLATE (cm)

Fig. l. Proton spectrum from the 21°Po(d, p)21ipo reaction. The z~~Po peaks are labeled according to table I. Impurity peaks are labeled with element symbol.

and to obtain spectroscopic factors for the transfer reaction, distorted wave Born approximation (DWBA) calculations were carried out. The D W B A code D W U C K 9) was used for these calculations. The potential parameters involved are given in table 2. These parameters have been used in ref. lo) for the (d, p) reaction on 2°8Pb. The cross section is given by

da-Ns(da)

dO

(t~ owucK"

The normalization factor N is 1.53 for the (d, p) reaction. The spectroscopic factor S is obtained by fitting the calculated angular distribution to the experimental distribution. The differences between angular distributions for different l, values are not great for the (d, p) reaction at 17 MeV. However, with the parameters used very good fits are obtained for the (d, p) reaction on :°SPb at the same energy t. Thus the small t The (d, p) reaction on 2°8pb was performed at 17 MeV for the purpose of normalization.

T. S. BHATIA et al.

104

TABLE 1 Levels of 211Po from 210po(d ' p)211Po Level no. 0 1 2 3 4 5 6 7 8 9

Excitation energy ( + 0.010 MeV) 0 0.685 1.049 1.120 1.155 1.378 1.436 1.799 2.022 2.084

I0

2.161

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

2.315 2.364 2.390 2.414 2.456 2.560 2.606 2.639 2.661 2.691 2.753 2.862 2.910 2.990 3.003 3.043 3.067 3.175 3.252 3.384 3.436 3.754 3.869 3.874

l. 4 6 2

2 (2) 2

lj tentative a)

S b)

g9/2 il 1..2 ds/2

0.89 0.95 0.28

ds/2 (ds/2 ds/2

0.08 0.05) 0.40

0

s~/2

0.56

(0)

(sl ,'2

0.20)

4 4 2

g'L,2 g7,,2 d3/2

0.29 0.12 0.13

4 2

g7/2 d3/2

0.32 0.51

2 (4)

d3/2

0.22

") See text. b) Spectroscopic factors assuming the orbit given in column 4.

d i f f e r e n c e s m a y be u t i l i z e d for levels w h e r e t h e statistical u n c e r t a i n t i e s a r e s m a l l e n o u g h to m a k e t h e d i s t i n c t i o n , a n d o n l y s u c h states a r e a s s i g n e d l n values. T h e res u i t i n g I, v a l u e s are g i v e n in t a b l e 1, c o l u m n 3. I n t h e N = 126 to N = 184 shell the l n = 4 states m a y be b o t h g~ a n d g ; a n d t h e I n = 2 states d~ a n d d~. I n c o l u m n 4 o f t a b l e 1 a t e n t a t i v e spin a s s i g n m e n t has b e e n m a d e p u r e l y o n t h e basis o f e x c i t a t i o n e n e r g y . O f t h e l n = 4 states o n l y t h e g r o u n d

209p0 ' 2 t tpo

Zl°Po(d,p) Z"Po • ~ort * long

5.0 • •

2.0

II

105

Ed= 17.0 MeV

run run

(12

1.0

0.1

(15

a5

/7-t'ktd

0.2

t J/TN.

cl )

(11

111

5.0'

ZO 1.0

1.0

~' (15

o.5 Qz

L= ia|

g OZ

tt t

~

(a) t t E

0.1

t

5.0

?

zo

(,,

1.0

0.~ 0.2

| | t ~

(4)

0.1

0

!

i

50

100

|

,o

'''\

10

~

0.5

i

0.1

0

1101

x~__

50

100

e lob (degrees)

Fig. 2. Angular distributions of protons from the 21°Po(d, p)211po reaction. Each distribution is labeled according to table I. The curves are DWBA calculations.

state is assigned g~ and the rest g_~. T h e l, = 2 states are assigned d~ below 1.8 M e V and d~ a b o v e 2.6 MeV. This is fairly arbitrary but with this choice the s u m m e d spectroscopic factors b e c o m e 0.89 for g~, 0.73 for g~, 0.81 for d~ and 0.86 for d~. T h e unassigned states would contribute ~ 1.2 as l, = 4 or ~ 0.6 as l, = 2 states, and thus with suitable assigments bring the total strength observed up to the same as that observed for 2°SPb(d, p)2°9pb.

106

T . S . B H A T I A et al.

mPo ( d , p ) alPo

Ed - 17.0 MeV

o

0.5

ti

i

[

, s ~ r t run long run

0.2

(11)

01

§ !

0.5"

SO

02

2.0 i

0.1

m

1.0

(12)

0.5

t ~

2.0

!

1.0

'5

|:1 | ~

05

(15) l t

E

~ O.S

ills

'u

t

| ! I

0.1

02i

c~6)

t

0.1

!

t

,20) i

t

G5

! o2 9 .1

t

!

(rt)

!

5.0

0.5

~

!

02

1.0

0.1

1

0

50

I

I

I

lOO e

lob ( d e g r e e s )

Fig. 3. As in fig. 2.

There is no clear candidate for an l. = 7 (Jzs/2) state. A state at . 1.0646 MeV has been observed by Faestermann e t al. ~ 3) to decay to the ground state with a halflife of 15.9 ns. This is consistent with an assignment for the state o f ~ - Such a state would contribute only insignificantly to the tail of our state at 1.049 MeV and thus our d a t a is inconclusive on this subject.

2°9p0, 211po

21°Po (d.p) ~IPo

107 Ed ,, 17.0 MeV

.short run

5.0

32

20 1.0 0.5 02

~ # (26)

0.1

o

0

(33) 0

t..

05

!

(27)

02 #

c~ 0.1 05 "0

o

(~)

02 0.1 50 20 1.0

0

,

i

50

100

i

0

SO

h

100

e lab ( degrees )

Fig. 4. As in fig. 2. 3.2. THE (d, t) AND (p, d) REACTIONS

An example of the triton spectra from the 21°Po(d, t) reaction is shown in fig. 5 and fig. 6 shows a deuteron spectrum from the (p, d) reaction. The excitation energies of levels excited in 2°9po in the two reactions are given in table 3. Angular distributions of tritons from the (d, t) reaction are shown in fig. 7 and of deuterons from the (p, d) reaction in fig. 8. D W B A calculations were also carried out for both reactions with

TABLE 2

108

Optical model parameters V

r

a

Ws

1.25 1.25 1.25

0.682 0.65 0.65

77.6 40.0

1.15 1.14 1.25

0.81 0.795 0.65

52.0

Wv

ri

ai

r~

1.25 1.25

0.783 0.76

1.30 1.25

~,

(d, p), (p, d) reactions b) d p n

- 112.0 - 52.0 a)

25

(d, t) reaction ~) d t n

- 105.0 - 169.6 ~)

1.34 1.48

- 12.0

1.25 1.40

0.69 0.824

32

a) A d j u s t e d to give correct b i n d i n g e n e r g y o f n e u t r o n . b) Ref. 1o). c) Refs. II, 12).

300

21°Po (d.t) ~09po

o 3p~z

E d = 17 MeV

x I16

e:

200

vi O 3Pvz X 116

so"

2f5/z

E

oE

3d

O

100

°

"1

°

11"

oQ"

.~

_ 110

115

i_ t25

120

DISTANCE ALONG PLATE (era) Fig. 5. T r i t o n spectrum from the 21°Po(d, t)2°gPo reaction. i

zl0 800 E E ¢'4 O

U3

i

Po ( p, d ) 20g Po Ep = 17.8 MeV

c~ 600

i x

400

o

~,,a = 58"

Ot

,It

200

88

90

92

94

DISTANCE ALONG PLATE (cm) Fig. 6. P r o t o n s p e c t r u m f r o m the 21°Po(p, d)2°9po reaction.

96

2O9po' 21 ~Po

109

TABLE 3 Levels of 2°9po from 2~°Po(d, t) and (p, d) reactions Exc. energy Level

(MeV +0.010 MeV)

0 1 2 3

0 0.547 0.857 1.174

4

1.214

5 6 7 8 9 10 11 12 13 14

1.765 1.996 2.061 2.082 2.186 2.206 2.239 2.339 2.363 2.664

(p, d)

(d, t)

j,t a)

½~(¢~-) ~

li

C2S

1

Pl/2 f5/2 P3/2 f5/2 P3/2 i13/2

2.10 6.31 3.24 0.41 0.55 9.67 0.55

1.05 1.05 0.81 0.07 0.14 0.69 0.07

1.72 0.75 0.81 1.50

0.22 0.09 0.11 0.19

3 1 3

1 (~+) ~-

C2S/(2J+ I) C2S/(2J+ 1)b)

l,

6 3 (3) (3) (3) (3) 3 3 3 3

f7/2

f7/2 fv/2

['7/2 f7/2

1.00 0.92 0.83 0.07 0.17

~) Ref. 16). b) Normalized to 1.00 for ground state.

the parameters given in table 2. The (d, t) parameters are derived from refs. ~1. 12) and have been used for the (t, d) reaction on 2°8pb [ref. 12)]. The (p, d) parameters are the same as for the (d, p) reaction. For the pickup reaction the cross section is

da

C2S /da'x

dr2 - N 2 J + l

[/~/DWUCK

with the normalization factor N = 3.33 for the (d, t) reaction. For the (p, d) reaction only relative spectroscopic factors were obtained. The distinction between In = 1 and I, = 3 distributions is not great. However for measurements with good statistics there are significant differences at the most forward angles and some difference in the slope at backward angles. The resulting l. values and spectroscopic factors are given in table 3. 4. Discussion 4.1. THE N U C L E U S 2°9po

The spectra of 2 ° 9 p o obtained in the neutron pickup reactions are very similar to those obtained for 2°Tpb in the same reactions on 2°8pb. The three very strong peaks in the low-energy part of the spectrum come at almost the same excitation energies (within 40 keV) as the p~, f~ and p~ states in 2°Tpb and very nearly exhaust

110

T. S. BHATIA et al.

21°po ( d, t ) 2°9p0

Ed = 17..0 MeV

5.0

/o

°/'~° °'~*^ o

2.0

oJo \

2,~

o...~..,

zis,,, v

,.,.

1.0 0.5

o\

2.0"

~"~

§'0

1.0

f

~ ~ e x .

/

0.5

,,A .t

F

0.1 '~

O.O5

2 f ~/ /l

2.339MeV

~ ...,t;-,o zf~ * "*-..~..- 2-3,,v

x • 1.17&Mti

5.0 2.0

C~

o

y

E

1.0

r

o

~Eex

\

~

,,.,

Q5

0.2

1.3

. 0.857 MtV

~ 2 1 4

- 2.206MW

t-3

MeV

0.1d

~ E

0.5

o

~O~o._

*°

0.2

~

• 2.166 MtV

1 113x ~z ~,,Eex . 1.766MeV

%

0.1

= 2.062 ItdeV

0.2

.,,,~..v o02 o~,, 0.0,

0.1 0.05

tlti

0.02

.

~ ~,~..~.~ ~

= 2.061 MeV

0.01 0

50

' 100

0 6 lab

5'0

' 100

( degrees )

Fig. 7. Angular distributions of tritons from the 2~Opo(d '

t)Z09po reaction.

2O9po' 21 'Po

111

ZmPo ( p,d ) 2°ePo Ep - 17.8 MeV

5.O 3p~

2010 ~

~

o

M.v

0.5 2f~ 1.0 f , , ~ . , - ~ , , ~ ] ~ . ? M e V

(15 .,~

0.2

2f;~

II

Eu .. 1.17&MoV

OJ

O05

5.O ap~

20

00

,of---

~

O.5

E~.O~7~v

3p M

,

0

50

100

g tab ( degrees ) Fig. 8. Angular distributions of protons from the 21°Po(p, d)2°9po reaction.

the single-particle strength of these orbits. The same is true of the weaker state at 1.765 MeV. It is populated through l. - 6 and carries most of the strength of the i~ 3/2 orbit. It is shifted up by 130 keV relative to 207Pb. The only other deviation from the 2°TPb spectrum in this low-energy part of the spectrum is the population of two states at 1.174 and 1.214 MeV with small amounts of l n = 3 and I. = 1 strength respectively. At higher excitation energies greater deviations from the 2°TPb spectrum are observed. A group of states is observed with l. = 3 transfer between 2.0 and 2.7 MeV. It is likely that they are all f~ states in this energy region. They then carry ~ 70~o

--h~

112

o

fT/2

r/z-

m r ~ C9 IZ LtJ Z ILl

--W

_7,/2 •

Z

_..---"

o

i~3/2

O+

ri-. x LIJ

__3/2- - p % -

......

- - f %

.......

--Pvz

.......

m

2*

- -

O÷

P~

P~/2

r~

f~

PV~

' P~/2 1

1

SPECTROSCOPIC FACTOR 2°:'Pb LEVELS

Z~°Po LEVELS EXPERIMENT

P.V •MODEL

Fig. 9. The result of a particle-vibration coupling calculation with the 2 + state of 21°po and the singlehole states P~2, fsJ2, P3/2, i13/2 and f7/2 compared with the experimental spectrum of 2°9p0. Only states with single-particle admixtures of > 1 ~o are shown in the calculated spectrum.

md~

>6,.9 (Z hi 21 IJJ Z O l-l--

- -

d3,~ 9r/2

- -

st&

=d 3/2 - ~---~9

7/2

- - "-----~-~$ V2

cj7/2 d s/2

r/;

s ',t

d% d% - -

J~%

X LIJ

.........

i~l/2

--gg/z

6" - - 4 *

~2"5/;

ds/2 - -

,J~

2" I IV2

'g~tt l SPECTROSCOPIC FACTOR

Z°gPb LEVELS

' gW= i

- -

O÷

='°Pc LEVELS

EXPERIMENT

P.V .MODEL

Fig. 10. The result of a particle-vibration coupling calculation with the 2 + state of 2 ~Opo and the singleparticle states of 2°9pb, compared with the experimental spectrum of 21~po. Only states with singleparticle admixtures of > 1 ~o are shown in the calculated spectrum. The Jls/z state is indicated with a dashed line because the experimental evidence is lacking. Unassigned weak states are indicated with dots in the experimental spectrum.

2°9po, 211po

113

of the f~ strength. The centroid of the observed states is at 2.37 MeV, only 30 keV from the f~ state of 2°Tpb. The differences between z°TPb and 2°9po are to be accounted for by the differences between the 2°spb and z~°Po cores. These differences arise from the two extra protons in 2~°po. This additional degree of freedom gives 21°po a set of states with spin and parity 2 ÷, 4 ÷, 6 ÷ and 8 + . Of these the 2 ÷ state is the one most likely to affect the single-particle motion. Coupling the 2 + state, which is found at 1.18 MeV, to the ground state p, hole would give two states at this energy with spin and parity k - and I - . These may be taken to be the two states observed at 1.174 and 1.214. The two states are observed through the admixture of p~ and f~ single-hole state respectively. These admixtures are given by the spectroscopic factors of table 3. A very simple calculation of such a coupling may be made by treating the 2 ÷ state as a shape vibration and using a particle-vibration coupling matrix element to calculate the admixtures. The matrix element used is that given in ref. 2) derived from the B(E) value. The result of such a calculation is given in fig. 9 together with the experimental spectrum. Treating the 2 ÷ state as a vibration is not the most realistic approach but the result shows that it yields very accurately both the admixed singlehole strength and the energy splitting of the two states. The more complex situation of the f~ strength is not accounted for by such a simple calculation. At this excitation energy additional core states as well as states based on other single-hole states may be involved. 4.2. THE NUCLEUS 211po

A similar simple particle-vibration coupling calculation may be carried out for 21Xpo" The calculation involves the 2 + state of 21°p0 and the particle states of 2°9pb. The results are shown in fig. 10 where they are compared with the experimental resuits. Here it is obvious that the calculation is inadequate but it may still serve as a basis for discussion. In the low-energy part of the spectrum a multiplet of states arising from the coupling of the ground state particle (g~) to the lowest core state (i.e. the 2 + state at 1.18 MeV) would be expected. The calculation predicts a certain admixture of d~ strength into the ~z+ member and a small amount of g~ into the ~+ member. A much larger fraction of the d~ strength is found in a state at 1.049 MeV. Thus the splitting of the strength is considerably larger than predicted. This may be contrasted with the corresponding situation in 21 ~pb where the same type of calculation predicts an admixture of 10 ~o of d~ strength into the multiplet state and none ( < 1 ~o) is observed in the experiment 14). For this case, where all three valence particles are neutrons, blocking will clearly play an important role. However even a calculation ~5) which take this into account, and also treats the particle core coupling in a more realistic way, overestimates the admixture by a factor of five. The remaining difference between the cases of 211Po and 211pb may be accounted for by a difference in neutron-neutron and proton-neutron interactions. The 2 + core states are pre-

114

T.S. BHATIA

et aL

d o m i n a n t l y p r o t o n excitations in 21°p0 a n d n e u t r o n e x c i t a t i o n s in 2 i ° p b a n d the effective i n t e r a c t i o n b e t w e e n p a r t i c l e a n d c o r e is e n h a n c e d o r reduced, respectively, by the isospin difference o f the i n t e r a c t i o n . A further i n d i c a t i o n o f the increased p a r t i c l e - c o r e i n t e r a c t i o n in 211p0 is given by the general stretching o f the s p e c t r u m o f 211po relative to 2°9pb. I f c e n t r o i d s are c a l c u l a t e d for the different n e u t r o n o r b i t s it is seen t h a t the high lying states (d~ a n d g~) c o m e 300-500 keV h i g h e r in 21 ~Po t h a n in 2°9pb. I f this viewed in t e r m s o f b i n d i n g energy it is seen t h a t the low lying states a r e b o u n d m o r e in 21 i p o t h a n in 2°9pb. T h u s the i n d i c a t i o n is t h a t the p a r t i c l e - c o r e i n t e r a c t i o n is increased for the low lying states, w h e r e a s this is n o t so effective for the h i g h e r lying states.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

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